You can do it with a keyboard shortcut attached to the macro ProcessSelectedMessage (or run SaveAttachments as a script from a rule as the messages arrive, which needs no shortcut or further user involvement)
Code:
Option Explicit
Sub ProcessSelectedMessage()
Dim olMsg As MailItem
On Error GoTo lbl_Exit
Set olMsg = ActiveExplorer.Selection.Item(1)
SaveAttachments olMsg
lbl_Exit:
Exit Sub
End Sub
Sub SaveAttachments(Item As Outlook.MailItem)
Dim olAtt As Attachment
Dim strFileName As String
Const strPath As String = "C:\Path\" 'The path where the files are to be saved
If Item.Attachments.Count > 0 Then
For Each olAtt In Item.Attachments
If Not olAtt.FileName Like "image*.*" Then
strFileName = strPath & olAtt.FileName
olAtt.SaveAsFile strFileName
End If
Next olAtt
End If
lbl_Exit:
Exit Sub
End Sub